论文信息 - Regular Cayley maps of skew-type 3 for abelian groups

Regular Cayley maps of skew-type 3 for abelian groups

Let M=CM(G,X,p) be a regular Cayley map, and let @f be the corresponding skew-morphism. If the power function of @f assumes exactly i values in Z"|"X"|, then M is called of skew-type i. Note that regular balanced Cayley maps are of skew-type 1, and regular t-balanced (including anti-balanced) Cayley maps are of skew-type 2. Those two classes of maps have been studied by many researchers. In this paper, some results on regular Cayley maps of skew-type 3 for abelian groups are given. As applications, many new regular Cayley maps for abelian groups are constructed.

Jun-Yang Zhang

[1] Thomas W. Tucker,et al. Cayley maps , 2005, J. Comb. Theory, Ser. B.

[2] Marston D. E. Conder,et al. Regular t-balanced Cayley maps , 2007, J. Comb. Theory, Ser. B.

[3] Yan Wang,et al. Regular Balanced Cayley Maps for Cyclic, Dihedral and Generalized Quaternion Groups , 2005 .

[4] Jin Ho Kwak,et al. A classification of regular t-balanced Cayley maps on dicyclic groups , 2008, Eur. J. Comb..

[5] Jozef Sirán,et al. Skew-morphisms of regular Cayley maps , 2002, Discret. Math..

[6] Young Soo Kwon,et al. A classification of regular t-balanced Cayley maps on dihedral groups , 2006, Eur. J. Comb..

[7] Martin Skoviera,et al. Regular maps from Cayley graphs III: t-balanced Cayley maps , 2007, Discret. Math..

[8] Young Soo Kwon,et al. Reflexibility of regular Cayley maps for abelian groups , 2009, J. Comb. Theory, Ser. B.

[9] Ju-Mok Oh. Regular t-balanced Cayley maps on semi-dihedral groups , 2009, J. Comb. Theory, Ser. B.

[10] Martin Skoviera,et al. Regular maps from Cayley graphs, part 1: Balanced Cayley maps , 1992, Discret. Math..

[11] Yan Wang,et al. Regular t-balanced Cayley maps for abelian groups , 2011, Discret. Math..

[12] Norman Biggs. Cayley maps and symmetrical maps , 1972 .

[13] Thomas W. Tucker,et al. Regular Cayley maps for finite abelian groups , 2007 .